论文信息 - A new iteration scheme for approximating fixed points of nonexpansive mappings

A new iteration scheme for approximating fixed points of nonexpansive mappings

In this paper, we introduce a new three-step iteration scheme and establish convergence results for approximation of fixed points of nonexpansive mappings in the framework of Banach space. Further, we show that the new iteration process is faster than a number of existing iteration processes. To support the claim, we consider a numerical example and approximated the fixed point numerically by computer using Matlab.

[1] Mujahid Abbas,et al. A new faster iteration process applied to constrained minimization and feasibility problems , 2014 .

[2] S. Reich. Weak convergence theorems for nonexpansive mappings in Banach spaces , 1979 .

[3] Z. Opial. Weak convergence of the sequence of successive approximations for nonexpansive mappings , 1967 .

[4] W. A. Kirk,et al. Topics in Metric Fixed Point Theory , 1990 .

[5] S. Stević. APPROXIMATING FIXED POINTS OF NONEXPANSIVE MAPPINGS , 2006 .

[6] Lu-Chuan Zeng,et al. A Note on Approximating Fixed Points of Nonexpansive Mappings by the Ishikawa Iteration Process , 1998 .

[7] Hong-Kun Xu,et al. Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process , 1993 .

[8] Jürgen Schu,et al. Iterative construction of fixed points of asymptotically nonexpansive mappings , 1991 .

[9] S. Ishikawa. Fixed points and iteration of a nonexpansive mapping in a Banach space , 1976 .

[10] Vasile Berinde,et al. Picard iteration converges faster than Mann iteration for a class of quasi-contractive operators , 2004 .

[11] S. Ishikawa. Fixed points by a new iteration method , 1974 .

[12] W. R. Mann,et al. Mean value methods in iteration , 1953 .

[13] J. Schu,et al. Weak and strong convergence to fixed points of asymptotically nonexpansive mappings , 1991, Bulletin of the Australian Mathematical Society.

[14] M. Noor. New approximation schemes for general variational inequalities , 2000 .